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Definition Links Links rule
binary
Last modified: December 14, 1997

Pertaining to a number system that has just two unique digits. For most purposes, we use the decimal number system, which has ten unique digits, 0 through 9. All other numbers are then formed by combining these ten digits. Computers are based on the binary numbering system, which consists of just two unique numbers, 0 and 1. All operations that are possible in the decimal system (addition, subtraction, multiplication, division) are equally possible in the binary system.

We use the decimal system in everyday life because it seems more natural (we have ten fingers and ten toes). For the computer, the binary system is more natural because of its electrical nature (charged versus uncharged).

In the decimal system, each digit position represents a value of 10 to the position's power. For example, the number 345 means:

3 three 100s (10 to the 2nd power)

plus

4 four 10s (10 to the first power)

plus

5 five 1s (10 to the zeroth power)

In the binary system, each digit position represents a power of 2. For example, the binary number 1011 equals:

1 one 8 (2 to the 3rd power)

plus

0 zero 4s (2 to the 2nd power)

plus

1 one 2 (2 to the first power)

plus

1 one 1 (2 to the zeroth power)

So a binary 1011 equals a decimal 11.

Because computers use the binary number system, powers of 2 play an important role. This is why everything in computers seems to come in 8s (2 to the 3rd power), 64s (2 to the 6th power), 128s (2 to the 7th power), and 256s (2 to the 8th power).

Programmers also use the octal (8 numbers) and hexadecimal (16 numbers) number systems because they map nicely onto the binary system. Each octal digit represents exactly three binary digits, and each hexadecimal digit represents four binary digits.

Decimal and Binary Equivalents

DecimalBinary
11
210
311
4100
5101
6110
7111
81000
91001
101010
1610000
32100000
641000000
1001100100
256100000000
5121000000000
10001111110100
102410000000000
See Also
binary format
decimal
hexadecimal
octal

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Legend

Data Representation Award Winning Page
This is Chapter 1 of Randall Hyde's book, "Art of Assembly Language." It describes the binary and hexadecimal numbering systems, binary data organization (bits, nibbles, bytes, words, and double words), signed and unsigned numbering systems, arithmetic, logical, shift, and rotate operations on binary values, bit fields and packed data, and the ASCII character set. Updated on Aug 5, 1998

Binary primer
Introduction to binary numbers.

Connected Encyclopedia's binary arithmetic overview
Explains binary arithmetic, bits, and bytes for beginners.

Data Representation - The Binary Number System
Very clear and concise discussion of the binary system used by computers to represent data. Updated on Apr 7, 1998

Learn to count in binary on your fingers
This page uses cartoon hands to demonstrate how to count on your fingers in binary. Though only the right hand is shown here, by "getting" the pattern, you can count to 1023 using both hands.

Lecture notes on binary numbers
These are notes on binary numbers and character sets from a computer architecture course. Updated on Jul 17, 1998

Representing data
This page explains binary representation of numbers in computers. Updated on Aug 4, 1998


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